Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/410

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378
COMPARISON OF UNITS.
[778.

rises from zero to its final value is expressed by a formula of exactly the same kind as that which expresses the value of a current urged by a constant electromotive force through the coil of an electromagnet. Hence we may place a condenser and an electromagnet on two opposite members of Wheatstone's Bridge in such a way that the current through the galvanometer is always zero, even at the instant of making or breaking the battery circuit.

In the figure, let , , , be the resistances of the four members of Wheatstone's Bridge respectively. Let a coil, whose coefficient of self-induction is be made part of the member , whose resistance is , and let the electrodes of a condenser, whose capacity is , be connected by pieces of small resistance with the points and . For the sake of simplicity, we shall assume that there is no current in the galvanometer , the electrodes of which are connected to and . We have therefore to determine the condition that the potential at may be equal to that at . It is only when we wish to estimate the degree of accuracy of the method that we require to calculate the current through the galvanometer when this condition is not fulfilled.

Let be the total quantity of electricity which has passed through the member , and that which has passed through at the time , then will be the charge of the condenser. The electromotive force acting between the electrodes of the condenser is, by Ohm's law, , so that if the capacity of the condenser is ,


.(1)


Let be the total quantity of electricity which has passed through the member , the electromotive force from to must be equal to that from to , or


.(2)


Since there is no current through the galvanometer, the quantity which has passed through must be also , and we find


.(3)


Substituting in (2) the value of , derived from (1), and com paring with (3), we find as the condition of no current through the galvanometer


.(4)